Can I add a supplier to more than 1 group?

You can only put one supplier in one group. You can however create another group as a 'super group' into which you can put any suppliers which cross over groups. For eg Group A- Sales, Group B- marketing and then the other group could be Sales & Marketing. You could have User #1 assigned to group A, User#2 to group B and then both assigned to Group C.

I have included a scenario below to help explain;

Looking at the Kitchen Group and the Bar Group below you can see that in theory they are wanting to add the crossed out suppliers to both groups, but as this isn't possible they can create a 'Super Group' with these suppliers in it and then add all of the 2 Groups Users to the Super Group. This works because even though a supplier cannot be added to more than 1 group, a User however can be added to multiple groups.

Note that this means all of these 3 suppliers invoices will be visible to both Group's Users and they will need to recognise which invoices are meant for them.